Brief Answer:
well... you have stopped it cold turkey.

Detailed Answer:
Most doses of hydrocodone (5 to 10 mg) would be out of the system in hours not days. The withdrawal would start by 24-36 hrs and peak by about 3 days. If someone were at 3 days after stopping hydrocodone and didn't have many symptoms (not counting a return of the pain for which they were taking the drug for in the first place!), then there isn't much of an issue.

Then.... the itching. Narcotics directly cause the release of histamine. This is not an allergy to them. People can have mild itching and not have it progress or do anything much. BUT this occurs ONLY when the drug is there and not when it isn't there (hours after the last dose it would go away. not days). So... with stopping and the itching gets WORSE means, not allergy or reaction to the drug. It is common for people to have some skin conditions with very MILD withdrawal. anti-histamines with mild sedatives with CLONIDINE might be helpful. Vistaril is generally used in this context. It has worked in the vast majority of these situations. Also, people who are on narcotics can have other conditions While one can have liver failure, cocaine abuse, scabies, severe IV drug abuse associated viral infections, etc.
Mostly, I've seen just mild anxiety and this causing itching that mild steroids or vistaril and/or a mild anti-depressant with some sedative properties can be really helpful.
Reaction to hydrocodone .. doesn't seem likely.
being off of it 3 days is the peak of withdrawal; symptoms are unlikely to get worse at day 4 onward. Might be some psychological effect of the drug or its withdrawal that WILL get better by day 4 onward. Cannot say in a particular person's case especially if the person is NOT seeming to have any psychological nor any drug problem whatsoever (implies there is an underlying medical condition causing the itching not related to the medication at all). Liver tests, blood count and blood protein and histamine analysis to look for signs of inflammation/allergy/infection or elevated bilirubin (liver failure/problem causes a pigment...bilirubin and bile salts.. to build up. it causes itching).

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Brief Answer:
would MOSTLY show it.

Detailed Answer:
but simple liver studies are cheaper and show problem/no problem. The simple labs do not show what is going on at all. Gallstones, if the liver just can't get rid of wastes, cirrhosis, iron overload, can be mostly proven by the ct, but labs would just show "liver having problems".
Then.... the ct can show really weird diseases like parasites, tuberculosis, tumors, that I'd never bring up because they are incredibly rare. All of these can cause Just Plain Itching and might not be found otherwise. I'd still do the bloodwork, but I think I've made a pretty good case for getting the ct's. Also, get the regular mammogram. Breast cancer can cause a lot of symptoms, but by the time the symptoms are all over, the tumor would be very widely spread and mostly visible just by looking let alone ct scan.

problems with the blood cells that contain histamine and other irritating compounds (the pink ones, the blue ones... 'eosinophils and basophils') can also cause itching and would mostly NOT show up on the CT.

Then, I'm assuming there isn't much visible on the skin. If there are HIVES or itchy spots, then it can be a skin reaction/allergy and pretty minor stuff.

Uncommonly, people can have senstive skin that gives hives with minor rubbing of the skin (and itching). but, this is generally very small areas (but the areas change) and people generally know they have this.

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